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%I #21 Mar 13 2023 06:04:55
%S 2,4,3,8,5,9,16,7,32,27,11,25,64,13,81,128,17,49,19,256,23,125,243,29,
%T 31,512,121,37,41,43,1024,729,169,47,343,53,625,59,61,2048,67,289,71,
%U 73,79,2187,361,83,89,4096,97,101,103,107,109,529,113,1331,3125,127
%N Cototients of consecutive pure powers of primes.
%C Cototients of prime powers do not remain always prime powers, but are primes if their exponent is 2.
%H Michael De Vlieger, <a href="/A053211/b053211.txt">Table of n, a(n) for n = 1..16384</a>
%H Michael De Vlieger, <a href="/A053211/a053211.png">Log log scatterplot of a(n)</a> n = 1..2^20, showing even a(n) in blue, 3 | a(n) in green, and prime a(n) in red, else black.
%F a(n) = A051953(A025475(n+1)) = cototient(p^k) = p^(k-1).
%e The 10th pure power of prime (but not a prime) is 81, so a(10) = 81 - EulerPhi(81) = 81 - 54 = 27. For n=p^2, a(n)=p.
%t Map[# - EulerPhi@ # &, Select[Range[16200], And[! PrimeQ@ #, PrimePowerQ@ #] &]] (* _Michael De Vlieger_, Jun 11 2018 *)
%t With[{nn = 2^14}, Map[Times @@ Map[#1^(#2 - 1) & @@ FactorInteger[#][[1]]] &, Select[Union@ Flatten@ Table[a^2*b^3, {b, nn^(1/3)}, {a, Sqrt[nn/b^3]}], PrimePowerQ] ] ] (* _Michael De Vlieger_, Mar 11 2023 *)
%Y Cf. A000010, A051953, A001248, A002618, A036689, A053650, A053191, A053192, A246547.
%K nonn
%O 1,1
%A _Labos Elemer_, Mar 03 2000
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